In recent years, with electronic apparatuses being rapidly made into light, thin and small in size, high density and high reliability are strongly demanded in packaging techniques, while LSI (Large Scale Integration) packages tend to be large in size and thin due to multi-pin for the purpose of high performance. Therefore, at the time of molding a plurality of LSI, warps occur in an LSI package while a mold resin is cured and contracted. Furthermore, in a reflow process of mounting these LSI packages on a printed wiring board, in addition to a warp occurring in molding, heat generated in the reflow process causes a mold resin and the printed wiring board to make complicated warping behavior. This warp might cause defective connection with solder at the time of reflow, which is a cause of large deterioration in connection reliability. Moreover, it is difficult to incorporate a warping printed wiring board into a thin casing, which is among factors in an increase in a proportion defective.
For solving the problem, related corporations, universities and research organizations have developed techniques aiming at first comprehending warping behavior at the time of reflow in advance and taking warp reduction measures at an upstream stage of designing because it is extremely hard to consider curing and contraction of a mold resin. In this technical development, because it is difficult to monitor warping behavior of an LSI package or a printed wiring board at a high temperature in experiment, various warping prediction techniques have been studied hard. Executed at an early stage is, as shown in non-patent Literature 1, a study of board warp prediction based on multilayered beam theory which is expansion of elastic beam theory and further executed is simulation using the Finite Element Method (FEM) for calculating a warp of a printed wiring board with an electronic component mounted, of which proposed is, for example, a system for calculating a warp of a printed wiring board by elasticity analysis as recited in Patent Literature 1. Moreover, as a highly precise prediction technique taking viscoelasticity of a resin used in a board or in an electronic component mounted thereon into consideration, proposed are FEM viscoelasticity analysis techniques as recited in non-patent Literature 2 and non-patent Literature 3.
The methods disclosed in the non-patent Literature 1 and Patent Literature 1 as the examples of the related technique are prediction techniques by elasticity analysis whose elasticity analysis results largely differ from actually measured warps, which fact is reported in the non-patent Literature 3. For solving the problem, it is necessary to take viscoelasticity of various kinds of resin materials used in a board or a component mounted thereon into consideration and to execute FEM viscoelasticity analyses recited in the non-patent Literature 2 and the non-patent Literature 3. In the viscoelasticity analysis methods used in the non-patent Literature 2 and the non-patent literature 3, analyses are made based on viscoelastic characteristics as of after curing in a resin material curing process. Therefore, non-patent Literature 4, which is one example of the related techniques, for example, recites an analysis method which enables a curing degree of the resin material (mold (curing degree<1), reflow (curing degree=1)) to be taken into consideration, which technique has made possible analyses taking a resin curing process into consideration.
Patent Literature 1: Japanese Patent Laying-Open No. 2004-013437.
Non-patent Literature 1: Juhachi Oda, “Analysis of Stress and Deflection of Printed Plate Board Using Multilayered Beam Theory”, Articles of Japan Society of Machinery Engineers, vol. 59, No. 563, pp. 203-208, 1993.
Non-patent Literature 2: K. Miyake, “Viscoelastic Warpage Analysis of Surface Mount Package”, Journal of Electronic Packaging, Vol. 123 (2001), pp. 101-104.
Non-patent Literature 3: Hirata and Hashiguchi, “Study of LSI-package Warp Deformation Using FEM Visco-elastic Simulation”, Mate 2005, pp. 329-332, 2005.
Non-patent Literature 4: Osamu Ina et al., “The Development of Simulation Technology of Heat Curing Processes of Resins”, Denso Technical Review, Vol. 7, No. 2. (2002), pp. 69-75.
Non-patent Literature 5: Miyake, “Thermo-Viscoelastic Analysis for Warpage of Ball Grid Array Packages Taking into Consideration of Chemical Shrinkage of Molding Compound”, Transactions of Japan Institute of Electronics Packaging, Vol. 7, No. 1 (2004), pp. 54-61.
The analysis methods whose one example is that recited in the non-patent Literature 4, however, is elasticity analysis, so that coexistence with viscoelasticity analysis is impossible. The reason is that because viscoelasticity and resin curing have been studied individually, no method has been found of coupling the individual time dependencies.
As an attempt to solve the above problem, reported so far is only the method recited in the non-patent Literature 5. This method, however, uses none of theoretical expressions of a resin curing degree as used in the non-patent Literature 4, in which method a change of a curing degree and resultant volume contraction are replaced by a change in a coefficient of linear expansion. Accordingly, since this method, when the coefficient of linear expansion is used as it is in the process of heating, causes a problem of expansion of resin volume to prevent consideration of curing and contraction, operation is executed of replacing the coefficient of linear expansion by a minus value. Furthermore, the coefficient of linear expansion is a parameter of temperature only and is not time-dependent. Therefore, this method uses only a temperature for the link with time-dependent viscoelasticity analysis, which is far from (time-dependent) viscoelasticity analysis taking a resin curing degree changing with a time history into consideration.